## What is RMS value? The easiest explantion.

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How many times we used the term RMS while dealing with AC circuits. Well, counting that is madness because we use it almost every day. The voltage we receive in our home is also a RMS value, the measurement of AC quantities given by multi meters is also a RMS value, the system voltages like 415V AC, 11kV AC, 36kV AC, etc are also RMS values, even, the values of power frequency withstand voltages given by IEC standards are also RMS values. The RMS value is an important term in electrical engineering. But, what is the exact meaning of RMS value? And why it is so much important? Well, if you have the same questions, you have clicked the right article. To get the easiest explanation of what is RMS value, read the article.

The use of RMS value is almost everywhere in electrical engineering, and every electrical engineer must know about RMS value. By the end of this article you will be able to understand what is the exact meaning of RMS value and you will also be able to explain the meaning of RMS value to your teachers, friends, colleagues.  So, let’s get started.

## Also watch the following video to understand more clearly.

We know that the voltage or current in case of DC systems never changes its direction. At every instance, it almost remains constant. And hence calculating power, voltage or current is very easy in DC systems. Consider the example shown in fig 1. Let’s say we have a 10V DC source which is connected to a bulb. And the current flowing through the circuit is 2A. From this we can easily calculate the power drawn by the bulb by simply multiplying the voltage with current, as both voltage and current are constant. And that will give us –

P =VI = 10 X 2 = 20W

Fig – 1

And this is the power taken by the bulb at any instance. Now, I will change the DC source with AC. The voltage and current are no more constant. The value of voltage and current will now change continuously. For easy understanding, we will only consider the voltage waveform (fig- 2). Voltage will start from  zero after some time it will reach to 5 V, after some time it will go to 10V, again after some time it reduce to 5V, 0V, -5V, -10V, -5V, 0V and the cycle continues (fig – 2).  And if we considering either 5V to -5V or 10V to -10V which is the peak to peak value or any other value of voltage on the waveform for power calculation, it will lead to the wrong value, because the value is only true for some particular time after that time the value is different.

Fig – 2

Things gets worse when we compare to different waveforms, for example if we are comparing sine wave with square wave, the sine wave will have its peak value for small amount of time than the square wave (fig-3) and hence the effect of these two AC voltages powering same load would be different.  So, considering the peak to peak values for calculations is not a good idea.

Fig – 3

So, we need a solution for this. We need a term which will give us the effective value of AC quantities which we can consider for power calculation and which will remain true for most of the time. Fortunately, we don’t have to worry, there is method to calculate the effective value in AC circuits. And how do we do it?

## Step 1 – Divide the waveform in equal section.

Simply mark the points on equal distance as shown. To understand we’ll consider only half cycle. You can also do it for second half cycle if you want.  The marked values are as shown.

## Step 2 – Take the square of each value.

Simply take the “square” of each value you marked.

## Step 3 – Take the Mean/average.

Simply take the “Mean” or average of the values.

## Step 4 – Square root.

Simply take the square “root” of the final value.

= √200

= 14.14 V rms

The value we get from this method is known as “RMS value” i.e. Root Mean Square value.

So, in our example the Peak value is 20 V, where the effective value or the RMS value is 14.14 V. This 14.14 V AC is equal to the 14.14V DC. Which means RMS value is equivalent to its DC value. To get the things more clearly consider the example shown. Here we have two different sources one is of 10 V RMS and other is 10 V DC, these sources are connected to the blub who has resistance of 2 ohms.  In case of DC circuit power dissipated is 50 W but(fig-4), what about AC (fig-5)? As the 10 V is a RMS value we can take it for the power calculation and power dissipated by AC circuit will also 50 W. And that’s why we need RMS value in case of AC.

Fig – 4

Fig – 5

RMS value is the best way to calculate the effective value of AC system. For instance, for calculating size of cable considering RMS current measurement is always helpful but, for considering insulator in high voltage AC applications Peak value shall be considered rather than RMS value.

RMS value, peak value, Average value will change with different waveforms. These values will be different for sine wave, for square wave, for triangular wave etc. To make things more easy, we also have a formula to calculate RMS value or peak value and it is given by –

V rms = 0.7071 x Vmax

Remember this value will remain true only for pure form of “sine wave”.

So, we can also calculate the RMS value in our using the formula and which will give us,

V rms = 0.7071 x 20 = 14.14 V

So, to summarize, RMS value is an effective value of AC quantities which needs to be considered for different types of calculations and assumption and it is also equivalent to its DC value.

So, guys that’s all for this article I’ll see you guys in my next one. Till then keep reading keep learning.

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Gaurav J. Completed Diploma and Bachelors degree in Electrical Engineering. Currently working with High Voltage Switchgear industry. Founded "www.theelectricalguy.in" in January 2017.

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